Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction

Kanyuta Poochinapan, Sompop Moonchai (), Tanadon Chaobankoh and Phakdi Charoensawan ()
Additional contact information
Kanyuta Poochinapan: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Sompop Moonchai: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Tanadon Chaobankoh: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Phakdi Charoensawan: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2025, vol. 13, issue 10, 1-24

Abstract: A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems.

Keywords: contraction; differential equation; integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/10/1569/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/10/1569/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:10:p:1569-:d:1652786

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().